The following magical sequence proves that Rydberg's, Planck's, Newton's, Coulomb's, etc. constants and formulas are all related through energy, and also confirms that the neutronic ratio (Rₙ) is a fundamental part of all of them.

Note: All the input data in these calculations has been provided by CalQlata's Constants page.

All calculations are the sole copyright priority of Keith Dixon-Roche © 2018

Keith Dixon-Roche is also responsible for all the other web pages on this site related to atomic theory

Watch this, it's magic!

Do you believe that Isaac Newton understood the mathematical laws of orbits?

Do you accept the Magnetic Constant?

μₒ = 4π . 1E-07 kg.m / C²

Do you accept the Permittivity Constant?

εₒ = 8.85418775855161E-12 C² / J.m

Permittivity is a ratio of electron magnetic charge displacement and electron magnetic field intensity, which is actually; C/m : J/C

εₒ = e² / 8.π.hꞌ = 8.85418775855161E-12 C² / J.m

Magnetic: Fₘ = G.m₁.m₂ / R² (Newton & Gilbert)

Electrical: Fₑ = k.q₁.q₂ / R² (Coulomb & Maxwell)

φ = Fₘ / Fₑ = G.mₚ.mₑ / k.e² = 4.40742111792334E-40

From which, we get, when replacing 'v' with 'c':

R = G.mₚ / φ.c² = 2.81793795383896E-15 m (Rₙ!)

So, we know that anything orbiting a proton at 'c' must be orbiting at 2.81793795383896E-15 m

'Rₙ' is therefore a constant that represents the orbital radius of an electron travelling at 'c'.

Newton and Coulomb both said so!

μₒ = 4π x 1E-07 kg.m/C²

but what is 1E-07?

mₑ.Rₙ/e² = 1.000000000000000E-07 kg.m/C²

Coincidence?

Coulomb's constant:

k = μₒ.c² / 4π = 8.98755184732667E+09 kg.m³ / C².s²

Incorporating μₒ we find:

k = mₑ.c².Rₙ / 4π.e² = 8.98755184732667E+09 kg.m³ / C².s²

k = (½.mₑ.c²) . (Rₙ/2π) / (e²) {kg.m³ / C².s² = kg.m²/s² . m / C² = J.m/C²}

Remember 'J.m/C²' when it comes to Planck's constant (h)

h = √[π.mₑ.aₒ / εₒ] = 6.62607174469163E-34 kg.m²/s

Planck claimed its units as 'J.s'

However, a frequency ratio must be applied to his formula to achieve these units:

h = √[π.mₑ.aₒ / εₒ] . **ƒ₁/ƒ₂** {kg.m²/s . **s/s**} (J.s)

h = √[4.π².mₑ².c².aₒ.Rₙ] = 6.62607174469163E-34 kg.m²/s

which can be reorganised thus:

h = √[aₒ.(4.π)² . Rₙ] . ½.mₑ.c² #

= 6.62607174469163E-34 kg.m²/s

i.e. average radius x kinetic energy! [but there is something missing #].

hꞌ = √[aₒ.(4.π)² . Rₙ] . ½.mₑ.c . v {kg.m²/s . m/s}

but what is v?

Let's try; vₒ = c . √[aₒ.(4.π)² . Rₙ] = 174090.866621084 m/s

hꞌ = 1.15353857232684E-28 kg.m³/s² {J.m}

but now the units work.

hꞌ = ½.mₑ.c² . Rₙ {J.m}

validating the modified version of Planck's constant (remember Coulomb's constant J.m/C²)

In this case; 'Rₙ' is not only the orbital radius of the electron when travelling at 'c', it is also the coincident electro-magnetic amplitude

(which is the purpose of Planck's constant).

Now if we try both constants to calculate the kinetic energy of an orbiting electron; Eᴾ using h & E using hꞌ ...

It appears that Planck's constant (h) doesn't work but hꞌ does!

But we have established a definite link between Coulomb's and Planck's constants.

Ṯ | R (A) | v | KE | Eᴾ (error) | E (error) |
---|---|---|---|---|---|

6.2332E+08 3.1166E+08 2.0777E+08 1.5583E+08 1.2466E+08 1.0389E+08 8.9045E+07 7.7915E+07 6.9257E+07 6.2332E+07 5.6665E+07 5.1943E+07 |
2.8179E-15 5.6359E-15 8.4538E-15 1.1272E-14 1.4090E-14 1.6908E-14 1.9726E-14 2.2544E-14 2.5361E-14 2.8179E-14 3.0997E-14 3.3815E-14 |
299792459 211985280.7 173085256.9 149896229.5 134071263.5 122389758.9 113310898.8 105992640.4 99930819.7 94802699.6 90390827.4 86542628.5 |
4.0936E-14 2.0468E-14 1.3645E-14 1.0234E-14 8.1871E-15 6.8226E-15 5.8479E-15 5.1170E-15 4.5484E-15 4.0936E-15 3.7214E-15 3.4113E-15 |
1.12193E-11 (274.1) 3.96662E-12 (193.8) 2.15915E-12 (158.2) 1.40241E-12 (137.0) 1.00348E-12 (122.6) 7.63376E-13 (111.9) 6.05785E-13 (103.6) 4.95828E-13(96.90) 4.15529E-13 (91.36) 3.54785E-13 (86.67) 3.07522E-13 (82.64) 2.69894E-13 (79.12) |
4.09356E-14 (1) 2.04678E-14 (1) 1.36452E-14 (1) 1.02339E-14 (1) 8.18711E-15 (1) 6.82259E-15 (1) 5.84794E-15 (1) 5.11694E-15 (1) 4.54840E-15 (1) 4.09356E-15 (1) 3.72141E-15 (1) 3.41130E-15 (1) |

Planck’s Energy (Eᴾ = h.ƒ)Note: the above (error) is a ratio and therefore a value of 1 represents zero error |

*ξᵥ* = vₒ:c

We can use this ratio (*ξᵥ*) to simplify Rydberg's wave number ...

R∞ = mₑ.e⁴ / 8.εₒ².h³.c = 10973726.9561359 /m

which becomes:

R∞ = 1 / aₒ.*ξᵥ* = 10973726.9561359 /m

To his own energy constant:

Rᵧ = R∞.h.c.(Z.n)² = Rₙ/aₒ . ½.mₑ.c² = 2.17987197684936E-18 J

By an amazing coincidence, it just happens to be the kinetic energy of an electron orbiting at 'aₒ' metres {Ṯ = 33192.4K}.

So, Rydberg was telling us that he defined an electron's rest-state to occur when orbiting at 'aₒ'.

aₒ = Rₙ . ½.mₑ.c² / Rᵧ {m}

So why do we refer to this dimension as Bohr's radius?

Because Bohr originally declared it to be the orbiting radius of a hydrogen electron at rest-mass; the only electron property he managed to calculate. He subsequently declared that electrons do not orbit (Quantum Theory) ...

... whereas Rydberg had actually told us that the orbital radius of an electron can be found from:

Rₑ / Rₙ = ½.mₑ.c² / KEₑ

which has subsequently proved to be correct, therefore Bohr was wrong, so we should be referring to 'aₒ' as the Rydberg radius.

Rₘ = Rₙ.*ξᵥ* = Rₙ / aₒ.R∞

Having already established that:

hꞌ = ½.mₑ.c² . Rₙ {J.m}

and:

R∞ = 1 / aₒ.*ξᵥ*

we have therefore, also established a definite working link between Planck's and Ryberg's constants.

hꞌ = e² / 8π.εₒ = ½.k.e² = 1.15353857232684E-28 {J.m}

It is interesting to note that using the modified version of Planck's constant we can find the fine-structure constant 'α':

2.hꞌ.εₒ = e² / 4π = 2.04272942122269E-39 C²

i.e. magnetic force = electrical force @ Rₙ

F = Rₙ².mₑ.c²/Rₙ³ = k.e²/Rₙ²

Rₙ = k.e² / mₑ.c² = 2.81793795383896E-15

{kg.m³.C² / C².s² / (kg.m²/s²) = m}

Confirming again that Coulomb said so.

kB = mₑ.c² / Y.Tₙ

i.e. the potential energy in a proton-electron pair at the time of its conversion to a neutron ...

... confirming that electrons orbit protons in circular paths.

After first discovering 'Rₙ' long-hand (iteratively), an unequivocal link between Newton's, Coulomb's, Planck's and Rydberg's constants has been established, all of which are dependent upon the neutronic radius.

'Rₙ' must, therefore be a real value that not only complies with known and accepted physical constants, it also validates those formula's in terms of their units and explains their meaning.

If we accept the validity of 'Rₙ' we must also accept the concept of circular orbits in atoms.

If we accept circular orbits in atoms, we must reject Quantum theory.

Moreover; Relativity invalidates the following accepted constants:

μₒ, εₒ, k, h, hꞌ, R∞, Rᵧ

because they all rely on 'Rₙ'

and, according to Relativity:

v = v / √[1+v/c] !

which means an electron could never achieve 'c'

(c = c/√2); so 'Rₙ' would be impossible

{c = c/√2 is of course nonsense because c ≠ c/√2}

You will find further reading on this subject in reference publications^{(73)}